Video surveillance systems or Internet of Multimedia Things (IoMT) are playing a more and more important role in our daily life. To obtain useful surveillance information timely and accurately, not only image recognition algorithm but also computing and communication resources can be bottlenecks of the whole system. In this work, taking face recognition application as an example, we study how to build video surveillance systems by utilizing mobile edge computing (MEC), one of the 5G's key technologies. Specifically, to achieve high recognition accuracy and low recognition time, we design image recognition algorithms for both the camera sensor and MEC server, and utilize Q-learning based approach to train actions of the system by jointly optimizing offloading decision and image compression parameter. Experiment results show the advantages of the proposed system design for enabling network-adaptive, efficient, and intelligent video surveillance.